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How do you get these numbers?
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I went to the
megamillions website and found the chances listed of hitting each of the prize levels (this is what another poster has placed in this thread) - I could have tried to calculate this, but I was lazy; since they are published, I figured they are accurate.
Then, for each prize level, I multiplied the chance of winning the prize times the amount of payout (e.g., at the easiest prize level, $2, this would be $2 * (1/75) = 0.02666666....). Finally, I summed up the output of these prize-level multiplications.
At $144 million, the resulting sum is $1.00141, which is slightly more than the $1.00 ticket price. With the current estimated payout for Friday night's drawing at $262 million, this value becomes about $1.6730.
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And for the possibility of duplicate numbers, i figure you only have to multiply the chance of hitting the jackpot times itself then multiply the amount of the jackpot to get your -EV for that event. Should only discount it by not that much.
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Hmmm...not sure if I agree here - I do agree that you need to perform some multiplication on your chance of winning the jackpot, but I do NOT think you should multiply it times itself. It seems that you should multiply it times the chance that two people choose the same 6 numbers, the probability of which is NOT the same as the chance of you getting the correct 6 numbers and winning the jackpot. Obviously, this chance goes up as more people play and it goes up pretty fast, actually (google: "Birthday Problem" for a similar situation - the chance of an event occurring goes up fairly dramatically the larger your sample) - I need some time to calculate the chance that two people choose the same set of numbers.